A windshield wiper blade turns through an angle of 135°. The bottom of the blade traces an arc with a 5-inch radius. The top of the blade traces an arc with a 22-inch radius. To the nearest inch, how much longer is the top arc than the bottom arc? Round to the nearest whole number.

Question

Mathematics

Bucky

31 October, 00:00

A windshield wiper blade turns through an angle of 135°. The bottom of the blade traces an arc with a 5-inch radius. The top of the blade traces an arc with a 22-inch radius. To the nearest inch, how much longer is the top arc than the bottom arc? Round to the nearest whole number.

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Answers (1)

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Braylon Carlson · Answer 1

The upper arc is longer than the lower arc by inches.

Step-by-step explanation:

Since both the arcs are made by the same wiper blade, hence the angle of the arc would be the same.

The radius of upper arc = 22 inch

The radius of the lower arc = 5 inch

Angle made by the arc = 135°

We know that length of the arc = (angle made/360) * 2πr

Where r is the radius of the arc

The difference in the arc length has been due to the difference in radius of the arcs.

Hence, the difference in the radius would be equal to the difference in arc length.

Difference in wiper radius = 22-5 = 17 inch

Putting the values together

arc length = (135/360) * 2*3.14*17

arc length = 40.035

The difference in arc length=40 inches (rounded off to the nearest whole number)